H∞ and H2 control of fractional models
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Christophe Farges
Abstract
This chapter is dedicated to the design of control laws for systems described by commensurate fractional-order models. Control specifications are formulated in terms of H∞ and H2 constraints on performance transfers of the closed-loop model. Two main approaches are proposed in order to design the control law. The first one consists in approximating the fractional-order model by an uncertain integer order model. The control law is then obtained using robust control design techniques. The second approach is to develop control design tools that are specific to fractional order models.
Abstract
This chapter is dedicated to the design of control laws for systems described by commensurate fractional-order models. Control specifications are formulated in terms of H∞ and H2 constraints on performance transfers of the closed-loop model. Two main approaches are proposed in order to design the control law. The first one consists in approximating the fractional-order model by an uncertain integer order model. The control law is then obtained using robust control design techniques. The second approach is to develop control design tools that are specific to fractional order models.
Chapters in this book
- Frontmatter I
- Preface V
- Contents VII
- Nonlinear control methods 1
- Dynamical properties of fractional models 29
- Modified versions of the fractional-order PID controller 57
- H∞ and H2 control of fractional models 73
- Stability analysis of discrete time distributed order LTI dynamic systems 101
- Continuous-time fractional linear systems: transient responses 119
- Continuous-time fractional linear systems: steady-state responses 149
- State space methods for fractional controllers design 175
- Posicast control of fractional-order systems 201
- FOMCON toolbox for modeling, design and implementation of fractional-order control systems 211
- FOTF Toolbox for fractional-order control systems 237
- Fractional-order controllers for mechatronics and automotive applications 267
- Fractional-order modeling and control of selected physical systems 293
- Control of a soft robotic link using a fractional-order controller 321
- Fractional-order precision motion control for mechatronic applications 339
- Development of fractional-order analog integrated controllers – application examples 357
- Synchronizations in fractional complex networks 379
- New trends in synchronization of fractional-order chaotic systems 397
- Index 423
Chapters in this book
- Frontmatter I
- Preface V
- Contents VII
- Nonlinear control methods 1
- Dynamical properties of fractional models 29
- Modified versions of the fractional-order PID controller 57
- H∞ and H2 control of fractional models 73
- Stability analysis of discrete time distributed order LTI dynamic systems 101
- Continuous-time fractional linear systems: transient responses 119
- Continuous-time fractional linear systems: steady-state responses 149
- State space methods for fractional controllers design 175
- Posicast control of fractional-order systems 201
- FOMCON toolbox for modeling, design and implementation of fractional-order control systems 211
- FOTF Toolbox for fractional-order control systems 237
- Fractional-order controllers for mechatronics and automotive applications 267
- Fractional-order modeling and control of selected physical systems 293
- Control of a soft robotic link using a fractional-order controller 321
- Fractional-order precision motion control for mechatronic applications 339
- Development of fractional-order analog integrated controllers – application examples 357
- Synchronizations in fractional complex networks 379
- New trends in synchronization of fractional-order chaotic systems 397
- Index 423
